Question

If x is 1, 2, or 3 and y is either 2 or 4, then the product xy can have how many different possible values?

• A. Three
• B. Four
• C. Five
• D. Six
• E. Seven

Hint:

For counting problems with small sets, creating a simple table or an organized list is the most reliable way to ensure you find all possibilities and correctly identify any duplicates.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem asks for the number of unique values that can be obtained by multiplying a number from a set \(X\) with a number from a set \(Y\). The key is to list all possible products and then count only the distinct (different) values.
Step 2: Detailed Explanation:
The possible values for \(x\) are \(\{1, 2, 3\}\).
The possible values for \(y\) are \(\{2, 4\}\).
Let's systematically calculate the product \(xy\) for every possible combination of \(x\) and \(y\).


If \(x = 1\):

\(1 \times 2 = 2\)
\(1 \times 4 = 4\)

If \(x = 2\):

\(2 \times 2 = 4\)
\(2 \times 4 = 8\)

If \(x = 3\):

\(3 \times 2 = 6\)
\(3 \times 4 = 12\)

Step 3: Identify Unique Values:
The list of all calculated products is \(\{2, 4, 4, 8, 6, 12\}\).
To find the number of different possible values, we list the unique values from this set:
\[ \{2, 4, 6, 8, 12\} \] The value 4 appears twice, but we only count it once.
Step 4: Final Answer:
By counting the elements in the set of unique values, we find there are 5 different possible values for the product \(xy\).